I have data (supposedly a volt-amper characteristic of some TTL component) which is:
U[V]: x := [ 0.25, 1.0, 1.4, 1.45, 1.50, 1.55, 1.6, 5.0]
I[mA]: y := [-0.85, -0.65, -0.54, -0.31, -0.1, -0.02, 0.0, 0.004]
I'd like to approximate this data using the least squares method, so that I can after get a "reasonably accurate" values for 0.8V and 3.5V. The approximated function should however be "reasonably well approximated" for other values too. The best accuracy for me wasn't even $ \epsilon = 0.1 $ (the error was something like 0.28),so anything beyond that is progress.
What I need is the functions, which will help me approximate this data. Getting the c-values (the multipliers for the functions) does not concern me, as I have a function that computes these sort-of optimally.
I've had some success trying to use these functions, but haven't been able to fit it properly and honestly I am out of ideas.
$$ f_{1} := -e^{-t^2} \\ f_{2} := -\frac{1}{t+1} \\ f_{3} := 1 $$
I would welcome any kind of help, I am struggling with even finding a function that would look at least something like this.